which is consistent with the formula for the mean volume of the Brownian plane hull, which can be derived from [1]}.
Lemma REF , together with [2]}, implies that for every \(r>0\) ,


P( |HtrQ(r)| > t ) t r(r+3)(r+1)3(r+2)34 (2r+3)2 t-3/2 .

Since we need a non-asymptotic upper bound valid for all \(r>0\)  and \(t>0\) , we prove the following weaker result:
